Theory of solitary plastic waves

The paper deals with the dislocation dynamics of coherently propagating modes of plastic shear (Lüders bands) in single crystals oriented for single slip, in terms of a generalized Fisher-Kolmogorov equation. The role of (1) cross-slip and (2) non-axial stresses as propagation mechnisms is investigated, and the problem of propagation velocity selection is addressed. The phenomenon of slip band clustering which was observed in sufficiently thick tensile specimens is traced back to a propagative instability owing to non-axial stresses.     

Theory of microplastic deformation of polycrystals in the stage of lüders band nucleation

This paper develops a model of microplastic deformation of a polycrystalline aggregate in the stage of Lüders band nucleation. The model is used in constructing a theory of microplastic deformation of polycrystals and in calculating the load diagram in the first stage of microdeformation; the proposed theory of a linear stress-strain relation is in accord with the experimental data. An expression is obtained for the coefficient of hardening in the first stage of microdeformaiton.Translated from Izvestiya Vysshkikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 14–18, October, 1981.     

Quantum mechanics of successive measurements with arbitrary meter coupling

We study successive measurements of two observables using von Neumann's measurement model. The two-pointer correlation for arbitrary coupling strength allows retrieving the initial system state. We recover Lüders rule, the Wigner formula and the Kirkwood-Dirac distribution in the appropriate limits of the coupling strength.     

An extensive 3D dislocation dynamics investigation of stage-I fatigue crack propagation

Stage-I fatigue crack propagation is investigated using 3D discrete dislocation dynamics (DD) simulations. Slip-based propagation mechanisms and the role of the pre-existing slip band on the crack path are emphasized. Stage-I crack growth is found to be compatible with successive decohesion of the persistent slip band/matrix interface rather than a mere effect of plastic irreversibility. Corresponding crack tip slip displacement magnitude and the associated crack growth rate are evaluated quantitatively at various tip distances from the grain boundary. This shows that grain boundaries systematically amplify slip dispersion ahead of the crack tip and consequently, slow down the stage-I crack growth rate. The results help in developing an original crack propagation model, accounting for the boundary effects relevant to polycrystals. The crack growth trend is then evaluated from calculations of the energy changes due to crack length increments. It is shown that the crack necessarily propagates by increments smaller than 10 nm.     

Stochastic dislocation patterning during cyclic plastic deformation

A dislocation dynamical theory is developed for the formation of dipole dislocation patterns during cyclic plastic deformation in single glide. The stochastic dislocation dynamics adopted is suitable to account, in terms of a fluctuating effective medium, for the effects of long-range dislocation interactions on a mesoscopic scale. The theory can explain the occurrence of a matrix structure and persistent slip bands as a result of evolutionary processes, it gives the intrinsic strain amplitudes and the characteristic wavelength of these structures, and it allows for an interpretation of the structural changes associated with changes of the deformation conditions. Quantitative results are in good agreement with experimental observations.     

Markov property of continuous dislocation band propagation

Tensile tests were carried out by deforming polycrystalline samples of substitutional Al–2.5%Mg alloy at room temperature for a range of strain rates. The Portevin–Le Chatelier (PLC) effect was observed throughout the strain rate regime. The deformation bands in this region are found to be of type A in nature. From the analysis of the experimental stress time series data we could infer that the dynamics of type A dislocation band propagation is a Markov process.     

Quantum conditional probability in one-dimensional scattering

A result of Wan and McLean on the asymptotic separation of states in quantum mechanics is used to analyze the motion of a particle across a one-dimensional potential of finite range in terms of quantum conditional probabilities. It is shown that probabilities conditional on transmission or reflection, defined according to the Lüders rule, yield the results to be expected by intuitive argument. The theorem of total probabilities, based on the events of transmission and reflection, is shown to hold for a class of observables, and examples are given both of observables which belong to this class and of observables which do not.     

Current theoretical approaches to collective behavior of dislocations

Plastic deformation is a highly dissipative process that induces a variety of patterns such as the cell structure in multislip conditions, the matrix structure and the persistent slip bands in cyclic deformation, as also the static and propagating bands in constant strain rate conditions. The diversity and the complexity of these patterns with length scales ranging from nanometers all the way to millimeters level, and time scales ranging from picoseconds to a few hours, pose serious challenges for modeling the collective behavior of dislocations. While a large body of knowledge has accumulated on the mechanics of dislocations and their interactions for a long time, describing such patterns has been slow mainly due to lack of methods to deal with the collective behavior of dislocations. The purpose of this review is to present the rich variety of dislocation patterns observed in different deformation conditions along with the recent advances in modeling using borrowed techniques traditionally used in condensed matter physics. These can be classified as statistical and dynamical approaches. The review begins with a summary of different types of patterns and their characterization. Appropriate background material is provided both in terms of basic dislocation mechanisms and theoretical methods. The latter includes the Langevin and distribution function approaches, and a host of standard dynamical methods such as the Ginzburg–Landau approach, methods of characterization of chaos and slow manifold analysis. Statistical models for the cell structure and persistent slip bands are based on Langevin dynamics and distribution function theoretic approaches. Of the dynamical models, the first set addresses the slowly emerging matrix structure and persistent slip bands. The second set of models is devoted to the study of a type of propagative instability called the Portevin–Le Chatelier effect. Generic features of the instability addressed include bistability, negative strain rate sensitivity of the flow stress, different types of bands, the dynamics and statistics of stress drops, and their characterization. Three different models all of which are dynamical in nature are discussed. While these models are quite different with regard to their frameworks, what they seek to describe and the levels of sophistication undertaken, these models capture a good variety of the observed features. The review ends with a summary and outlook.     

Continual model of the production of Lüders bands in polycrystalline materials

The effect of plastic-deformation gradients in front of a grain boundary on the stress concentration is analyzed. The stress of the production of a Lüders band is calculated and it is shown that it depends on the grain size.Institute of Physics of Strength and Study of Materials. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 15–21, May, 1995.     

Projecting low and extensive dimensional chaos from spatio-temporal dynamics

We review the spatio-temporal dynamical features of the Ananthakrishna model for the Portevin-Le Chatelier effect, a kind of plastic instability observed under constant strain rate deformation conditions. We then establish a qualitative correspondence between the spatio-temporal structures that evolve continuously in the instability domain and the nature of the irregularity of the scalar stress signal. Rest of the study is on quantifying the dynamical information contained in the stress signals about the spatio-temporal dynamics of the model. We show that at low applied strain rates, there is a one-to-one correspondence with the randomly nucleated isolated bursts of mobile dislocation density and the stress drops. We then show that the model equations are spatio-temporally chaotic by demonstrating the number of positive Lyapunov exponents and Lyapunov dimension scale with the system size at low and high strain rates. Using a modified algorithm for calculating correlation dimension density, we show that the stress-strain signals at low applied strain rates corresponding to spatially uncorrelated dislocation bands exhibit features of low dimensional chaos. This is made quantitative by demonstrating that the model equations can be approximately reduced to space independent model equations for the average dislocation densities, which is known to be low-dimensionally chaotic. However, the scaling regime for the correlation dimension shrinks with increasing applied strain rate due to increasing propensity for propagation of the dislocation bands. The stress signals in the partially propagating to fully propagating bands turn to have features of extensive chaos.     

Intermittency at the edge of a stochastically inhibited pattern-forming instability

A layer of ferrofluid under a static vertical magnetic field is submitted to a random vertical vibration which acts as a multiplicative noise on the Rosensweig instability. At low noise amplitude the Rosensweig instability onset is delayed and our experimental results are in good agreement with the theoretical prediction of Lücke et al. [1]. For larger noise, a new regime is found where peaks appear and vanish randomly in time. Statistical properties of the temporal evolution of the fluid surface are presented.Received: 6 March 2003, Published online: 11 August 2003PACS: 47.54.+r Pattern selection; pattern formation - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion     

Visualization of inhomogeneities in a plastic flow by the fields of decorrelation and scintillation rates of video speckles

We consider the algorithms of in situ methods for visualizing the localization zones of plastic deformation, as well as experimental dependences of visualizing signals and parameter (which are inversely proportional to the quality of measurements) on the deformation being visualized. Typical examples of the result of visualization of a plastic flow are given in the case of propagation of Chernov-Lüders bands.     

Lévy flights in inhomogeneous environments

We study the long time asymptotics of probability density functions (pdfs) of Lévy flights in confining potentials that originate from inhomogeneities of the environment in which the flights take place. To this end we employ two model patterns of dynamical behavior: Langevin-driven and (Lévy-Schrödinger) semigroup-driven dynamics. It turns out that the semigroup modeling provides much stronger confining properties than the standard Langevin one. For computational and visualization purposes our observations are exemplified for the Cauchy driver and its response to external polynomial potentials (referring to Lévy oscillators), with respect to both dynamical mechanisms. We discuss the links of the Lévy semigroup motion scenario with that of random searches in spatially inhomogeneous media.     

Propagation dynamic of a Gaussian in the inverted nonlinear photonic crystals

In this work, we study the evolution of a Gaussian beam inside a one-dimensional inverted nonlinear photonic crystals (INPC) with a Kerr nonlinearity. The INPC is a kind of virtual crystals which is generated by the optical induction via the electromagnetically induced transparency (EIT). The propagation dynamics of the Gaussian with different total power are identified. Four types of propagation behavior are found. They are collapse beam, breather beam, soliton and symmetry-breaking beam, respectively. The border between these four behavior types are given. For symmetry-breaking beam, an asymmetric profile of the beam is evolving from the symmetry Gaussian, which can be termed as a kind of dynamical symmetry breaking (DSB). The influences on the appearance of the symmetry breaking point are studied by varying input parameters of the Gaussian. The results of this work are both suitable in nonlinear optics and Bose-Einstein condensate (BEC).     

Stability Diagrams of a Bose-Einstein Condensate in Excited Bloch Bands

Landau and dynamical instabilities o/a Bose-Einstein condensate （BEC） in the excited bands of a one-dimensional optical lattice are investigated by the Gross Pitaevskii theory. Our results show that there always exists Landau instability for a BEC in the whole region of excited bands. We also map out the dangerous zones of the dynamical instability. The experimental implications of the stability diagram are discussed.     

The melting behaviors of the Nb(1 1 0) nanofilm: a molecular dynamics study

By using molecular dynamics (MD) and the modified analytic embedded atom method (MAEAM), we have studied the melting point, the melting mechanism and the correspondingly dynamical behaviors of a Nb(1 1 0) nanofilm. Firstly, in accordance to the MD time dependence of the potential energy, the melting point of this nanofilm has been roughly estimated. Then, the melting mechanism of the nanofilm have been analyzed in detail with the application of the structure factor. The results clearly indicate that the melting transition of the 8th, 9th, and 10th atomic layer of the nanofilm has been characterized by the exponential, polynomial and linear sequence respectively when the thickness of the quasiliquid film attains to about 1.3 nm. Thirdly, the dynamical behaviors of the nanofilm melting, such as the melting front propagation velocity and the kinetic coefficient, which have also been analyzed, demonstrate that the melting front propagation velocity has linearly increased with the incremental temperature and the evaluated kinetic coefficient has approximately equaled 1.43m/(sK). Finally, by extrapolating the melting front propagation velocity to zero, we can accurately deduce the melting point of the Nb(1 1 0) nanofilm to 2568.3 K, which is much lower than the counterpart (2740 K) of the bulk niobium.     

Adaptive projective synchronization in complex networks with time-varying coupling delay

In this Letter, adaptive projective synchronization (PS) between two complex networks with time-varying coupling delay is investigated by the adaptive control method, and this method has been applied to identify the exact topology of a weighted general complex network. To validate the proposed method, the Lü and Qi systems as the nodes of the networks are detailed analysis, and some numerical results show the effectiveness of the present method.     

Optical absorption of 1,3-diphenyl-1H-Pyrazolo[3,4-b]quinoline and its derivatives

Paper deals with the experimental investigations and quantum chemical calculations of the absorption spectra of newly synthesized 1,3-diphenyl-1H-Pyrazolo[3,4-b]quinoline and its 6-Vinyl, 6-N,N-Diphenyl, 6-Methyl, 6-Fluoro, 6-Bromo, and 6-Chloro derivatives. The calculations are performed by means of the semiempirical quantum chemical methods AM1 or PM3 combined with: (a) equilibrium molecular conformation (EMC) in vacuo; (b) the molecular conformation model considering a dynamical rotation of phenyl rings only (T = 300 K); and (c) the most general model of the conformational molecular dynamics (MD) at T = 300 K. It is shown that the phenyl dynamics appears to be not important in the spectral position of absorption thresholds as well as in a broadening of most absorbtion bands. On the other hand, the MD simulations reproduce a broadening of the absorbtion spectra as well as the electron-vibronic coupling leading to a red-shift of absorption bands with increasing of temperature. The conformational MD model in combination with the quantum chemical AM1 method gives in most cases the best agreement with the experimental data, namely in the sense of spectral positions and width of the absorption bands including first oscillators (absorption thresholds).     

The effect of the location of stage-I fatigue crack across the persistent slip band on its growth rate – A 3D dislocation dynamics study

Abstract

A 3D dislocation dynamics study to ascertain the probable path of stage-I fatigue crack propagation across the persistent slip band (PSB) in austenitic stainless steel is presented. Cyclic plasticity and the resulting crack tip slip displacement (CTSD) are evaluated for cracks of varying length introduced at PSB-center and at two PSB-matrix interfaces. CTSD attains high value at either of the two interfaces irrespective of the proximity of crack front to the grain boundary. Further, a difference in microcrack propagation rate is also observed among the two interfaces. The present results assert microcrack propagation preferrentially along one of the two PSB-matrix interfaces rather than at the PSB-center. A pre-existing PSB dislocation structure localises the cyclic slip for crack lengths up to approximately half of the grain depth for an applied strain range of 2 × 10^?4.